18,642 research outputs found
Staggered Chiral Perturbation Theory
We discuss how to formulate a staggered chiral perturbation theory. This
amounts to a generalization of the Lee-Sharpe Lagrangian to include more than
one flavor (i.e. multiple staggered fields), which turns out to be nontrivial.
One loop corrections to pion and kaon masses and decay constants are computed
as examples in three cases: the quenched, partially quenched, and full
(unquenched) case. The results for the one loop mass and decay constant
corrections have already been presented in Ref. [1].Comment: talk presented by C. Aubin at Lattice2002(spectrum); 3 pages, 1
figur
Generalised L\"uroth expansions and a family of Minkowski's Question-Mark functions
The Minkowski's Question-Mark function is a singular homeomorphism of the
unit interval that maps the set of quadratic surds into the rationals. This
function has deserved the attention of several authors since the beginning of
the twentieth century. Using different representations of real numbers by
infinite sequences of integers, called -L\"uroth expansions, we obtain
different instances of the standard shift map on infinite symbols, all of them
topologically conjugated to the Gauss Map. In this note we prove that each of
these conjugations share properties with the Minkowski's Question-Mark
function: all of them are singular homeomorphisms of the interval, and in the
"rational" cases, they map the set of quadratic surds into the set of rational
numbers. In this sense, this family is a natural generalisation of the
Minkowski's Question-Mark function
Comment on "Chiral anomalies and rooted staggered fermions"
In hep-lat/0701018, Creutz claims that the rooting trick used in simulations
of staggered fermions to reduce the number of tastes misses key physics
whenever the desired theory has an odd number of continuum flavors, and uses
this argument to call into question the rooting trick in general. Here we show
that his argument fails as the continuum limit is approached, and therefore
does not imply any problem for staggered simulations. We also show that the
cancellations necessary to restore unitarity in physical correlators in the
continuum limit are a straightforward consequence of the restoration of taste
symmetry.Comment: 11 pages, version 3 (4/13/07): Revisions to correspond to Creutz's
latest posting, including a change in the title. Version to appear in Physics
Letters
"Audacity or Precision": The Paradoxes of Henri Villat's Fluid Mechanics in Interwar France
In Interwar France, Henri Villat became the true leader of theoretical
researches on fluid mechanics. Most of his original work was done before the
First World War; it was highly theoretical and its applicability was
questioned. After having organized the first post-WWI International Congress of
Mathematicians in 1920, Villat became the editor of the famous Journal de
math\'ematiques pure et appliqu\'es and the director of the influential book
series "M\'emorial des sciences math\'ematiques." From 1929 on, he held the
fluid mechanics chair established by the Air Ministry at the Sorbonne in Paris
and was heading the government's critical effort invested in fluid mechanics.
However, while both his wake theory and his turbulence theory seemingly had
little success outside France or in the aeronautical industry (except in the
eyes of his students), applied mathematics was despised by the loud generation
of Bourbaki mathematicians coming of age in the mid 1930s. How are we to
understand the contrasted assessments one can make of Villat's place in the
history of fluid mechanics
Staggered Chiral Perturbation Theory at Next-to-Leading Order
We study taste and Euclidean rotational symmetry violation for staggered
fermions at nonzero lattice spacing using staggered chiral perturbation theory.
We extend the staggered chiral Lagrangian to O(a^2 p^2), O(a^4) and O(a^2 m),
the orders necessary for a full next-to-leading order calculation of
pseudo-Goldstone boson masses and decay constants including analytic terms. We
then calculate a number of SO(4) taste-breaking quantities, which involve only
a small subset of these NLO operators. We predict relationships between SO(4)
taste-breaking splittings in masses, pseudoscalar decay constants, and
dispersion relations. We also find predictions for a few quantities that are
not SO(4) breaking. All these results hold also for theories in which the
fourth-root of the fermionic determinant is taken to reduce the number of quark
tastes; testing them will therefore provide evidence for or against the
validity of this trick.Comment: 39 pages, 6 figures (v3: corrected technical error in enumeration of
a subset of NLO operators; final conclusions unchanged
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